What are the divisors of 4881?

1, 3, 1627, 4881

There is a total of 4 positive divisors.
The sum of these divisors is 6512.
The arithmetic mean is 1628.

4 odd divisors

1, 3, 1627, 4881

How to compute the divisors of 4881?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 4881 by each of the numbers from 1 to 4881 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

4881 / 1 = 4881 (the remainder is 0, so 1 is a divisor of 4881)
4881 / 2 = 2440.5 (the remainder is 1, so 2 is not a divisor of 4881)
4881 / 3 = 1627 (the remainder is 0, so 3 is a divisor of 4881)
...
4881 / 4880 = 1.0002049180328 (the remainder is 1, so 4880 is not a divisor of 4881)
4881 / 4881 = 1 (the remainder is 0, so 4881 is a divisor of 4881)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 4881 (i.e. 69.864153898834). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

4881 / 1 = 4881 (the remainder is 0, so 1 and 4881 are divisors of 4881)
4881 / 2 = 2440.5 (the remainder is 1, so 2 is not a divisor of 4881)
4881 / 3 = 1627 (the remainder is 0, so 3 and 1627 are divisors of 4881)
...
4881 / 68 = 71.779411764706 (the remainder is 53, so 68 is not a divisor of 4881)
4881 / 69 = 70.739130434783 (the remainder is 51, so 69 is not a divisor of 4881)